## Heatmap: Category Distribution Across Layers and Heads ### Overview The image presents a series of heatmaps visualizing the distribution of different categories (Algorithmic, Knowledge, Linguistic, Translation, and Unclassified) across various layers and heads of a model. The heatmaps are arranged side-by-side, with one showing the distribution of all categories combined and the others showing the distribution of each individual category. The x-axis represents the layer number, and the y-axis represents the head number. ### Components/Axes * **X-axis (Layer):** Represents the layer number, ranging from 0 to 30 with increments of 6. * **Y-axis (Head):** Represents the head number, ranging from 0 to 30 with increments of 6. * **Heatmap Cells:** Each cell represents a specific layer and head combination. The color of the cell indicates the category or combination of categories present at that location. * **Legend (All Categories Plot):** Located to the right of the "All Categories" heatmap. * **Unclassified:** Not explicitly represented by a color, but implied to be the background color (light gray). * **Algorithmic:** Blue * **Knowledge:** Orange * **Linguistic:** Green * **Translation:** Red * **2 categories:** Purple * **3 categories:** Brown * **4 categories:** Pink ### Detailed Analysis **1. All Categories** * This heatmap shows the combined distribution of all categories. * The distribution is sparse, with most cells being unclassified (light gray). * Several cells contain multiple categories, indicated by the purple, brown, and pink colors. * **Specific Data Points:** * Layer 18, Head 18: Linguistic (Green) * Layer 24, Head 12: Translation (Red) * Layer 24, Head 18: 3 categories (Brown) * Layer 24, Head 24: 2 categories (Purple) * Layer 24, Head 30: Linguistic (Green) * Layer 30, Head 0: Algorithmic (Blue) * Layer 30, Head 18: Linguistic (Green) * Layer 30, Head 24: Algorithmic (Blue) * Layer 30, Head 30: Linguistic (Green) **2. Algorithmic** * This heatmap shows the distribution of the "Algorithmic" category (Blue). * The distribution is sparse, with most cells being unclassified. * **Specific Data Points:** * Layer 0, Head 0: Algorithmic (Blue) * Layer 18, Head 12: Algorithmic (Blue) * Layer 18, Head 18: Algorithmic (Blue) * Layer 18, Head 24: Algorithmic (Blue) * Layer 18, Head 30: Algorithmic (Blue) * Layer 24, Head 12: Algorithmic (Blue) * Layer 24, Head 18: Algorithmic (Blue) * Layer 24, Head 24: Algorithmic (Blue) * Layer 30, Head 0: Algorithmic (Blue) * Layer 30, Head 24: Algorithmic (Blue) **3. Knowledge** * This heatmap shows the distribution of the "Knowledge" category (Orange). * The distribution is sparse, with most cells being unclassified. * **Specific Data Points:** * Layer 6, Head 18: Knowledge (Orange) * Layer 18, Head 0: Knowledge (Orange) * Layer 18, Head 18: Knowledge (Orange) * Layer 18, Head 24: Knowledge (Orange) * Layer 24, Head 18: Knowledge (Orange) **4. Linguistic** * This heatmap shows the distribution of the "Linguistic" category (Green). * The distribution is relatively more dense compared to other categories. * **Specific Data Points:** * Layer 0, Head 18: Linguistic (Green) * Layer 0, Head 24: Linguistic (Green) * Layer 6, Head 18: Linguistic (Green) * Layer 12, Head 18: Linguistic (Green) * Layer 12, Head 24: Linguistic (Green) * Layer 12, Head 30: Linguistic (Green) * Layer 18, Head 0: Linguistic (Green) * Layer 18, Head 12: Linguistic (Green) * Layer 18, Head 18: Linguistic (Green) * Layer 18, Head 24: Linguistic (Green) * Layer 18, Head 30: Linguistic (Green) * Layer 24, Head 0: Linguistic (Green) * Layer 24, Head 18: Linguistic (Green) * Layer 24, Head 30: Linguistic (Green) * Layer 30, Head 18: Linguistic (Green) * Layer 30, Head 30: Linguistic (Green) **5. Translation** * This heatmap shows the distribution of the "Translation" category (Red). * The distribution is very sparse, with only a few cells classified. * **Specific Data Points:** * Layer 12, Head 24: Translation (Red) * Layer 18, Head 30: Translation (Red) * Layer 24, Head 30: Translation (Red) ### Key Observations * The "Linguistic" category appears to be the most prevalent, with a relatively dense distribution across layers and heads. * The "Translation" category is the least prevalent, with only a few occurrences. * Several layer-head combinations contain multiple categories, suggesting that these locations are involved in processing multiple types of information. * The distributions of individual categories are sparse, indicating that each category is primarily associated with specific layers and heads. ### Interpretation The heatmaps provide insights into how different categories of information are processed within the model. The varying distributions suggest that different layers and heads specialize in processing specific types of information. The presence of multiple categories in some layer-head combinations indicates that these locations may be involved in integrating information from different categories. The relative prevalence of the "Linguistic" category suggests that the model is heavily focused on processing linguistic information. The sparsity of the "Translation" category may indicate that the model relies on other categories to perform translation tasks or that translation-specific processing is concentrated in a few specific locations.

## Heatmaps: Layer vs. Head Activation by Category ### Overview The image presents five heatmaps, each visualizing the activation levels of different categories (Algorithmic, Knowledge, Linguistic, Translation, and All Categories) across layers (0-32) and heads (0-32). The activation level is represented by color intensity, with a legend indicating the number of categories present at each point. The heatmaps aim to show where different categories are most active within the model's layers and heads. ### Components/Axes * **X-axis (Layer):** Represents the layer number, ranging from 0 to 32, with increments of 2. * **Y-axis (Head):** Represents the head number, ranging from 0 to 32, with increments of 6. * **Color:** Represents the number of categories activated at a given layer and head. The legend indicates: * 1 category: Lightest color (appears white/very pale) * 2 categories: Light blue/green * 3 categories: Medium blue/green * 4 categories: Darkest color (dark green) * **Heatmaps:** Five separate heatmaps, each focusing on a specific category or all categories. * "All Categories" * "Algorithmic" * "Knowledge" * "Linguistic" * "Translation" ### Detailed Analysis or Content Details **1. All Categories:** * The heatmap shows a dense distribution of activations across layers and heads. * The highest activation (4 categories) is concentrated around layers 18-24 and heads 6-18. * There's a noticeable cluster of 3-category activations around layers 0-6 and heads 0-12. * Lower activations (1-2 categories) are scattered throughout the remaining areas. **2. Algorithmic:** * Activations are primarily concentrated in layers 0-24. * The highest activation (4 categories) is not present. * The most frequent activation level is 2 categories, observed around layers 6-18 and heads 0-12. * A sparse distribution of 1 and 3 category activations is visible. **3. Knowledge:** * Activations are concentrated in layers 18-24. * The highest activation (4 categories) is present in a small region around layer 24 and head 0-6. * The majority of activations are at the 2 and 3 category levels, distributed across layers 18-24 and heads 0-18. **4. Linguistic:** * Activations are heavily concentrated in layers 18-30. * The highest activation (4 categories) is present around layers 18-24 and heads 0-12. * A significant number of 3-category activations are observed across layers 18-30 and heads 0-18. * Lower activations (1-2 categories) are scattered throughout. **5. Translation:** * Activations are primarily concentrated in layers 18-30. * The highest activation (4 categories) is present around layers 18-24 and heads 0-6. * A strong cluster of 3-category activations is observed around layers 24-30 and heads 0-12. * The heatmap shows a relatively sparse distribution of 1 and 2 category activations. ### Key Observations * The "All Categories" heatmap shows the most widespread activation, indicating a general level of activity across all layers and heads. * "Algorithmic" activations are relatively sparse and concentrated in the earlier layers. * "Knowledge," "Linguistic," and "Translation" categories exhibit stronger activations in the later layers (18-30). * The "Translation" category shows a distinct concentration of activations in the higher layers, suggesting that translation-related processing occurs later in the model. * The "Linguistic" category has a broad distribution of activations, indicating its involvement across multiple layers and heads. ### Interpretation The heatmaps suggest a hierarchical processing structure within the model. Earlier layers (0-18) seem to handle more general or "algorithmic" features, while later layers (18-30) are more specialized in processing "knowledge," "linguistic," and "translation" information. The concentration of "Translation" activations in the higher layers supports the idea that translation is a more complex process that builds upon lower-level linguistic representations. The varying levels of activation across categories and layers provide insights into the model's internal representations and how different types of information are processed. The "All Categories" heatmap serves as a baseline, showing the overall activity level, while the individual category heatmaps reveal the specific contributions of each category to the model's overall behavior. The presence of 4-category activations in specific regions suggests areas where multiple features or concepts are strongly represented, potentially indicating key processing nodes.

## Heatmap Series: Attention Head Specialization Across Model Layers ### Overview The image displays a series of five horizontally arranged heatmaps that visualize the classification of attention heads within a neural network model (likely a transformer) across its layers. Each heatmap plots "head" index (y-axis) against "layer" index (x-axis), with colored squares indicating heads assigned to specific functional categories. The first plot aggregates all classifications, while the subsequent four plots isolate individual categories. ### Components/Axes * **Common Axes (All Plots):** * **X-axis:** Labeled "layer". Scale ranges from 0 to 30, with major tick marks at 0, 6, 12, 18, 24, 30. * **Y-axis:** Labeled "head". Scale ranges from 0 to 30, with major tick marks at 0, 6, 12, 18, 24, 30. * **Legend (Positioned to the left of the first plot):** * **4 categories:** Pink square * **3 categories:** Brown square * **2 categories:** Purple square * **Translation:** Red square * **Linguistic:** Green square * **Knowledge:** Orange square * **Algorithmic:** Blue square * **Unclassified:** Gray square (This also serves as the background color for all plots). * **Plot Titles (Positioned above each heatmap):** 1. All Categories 2. Algorithmic 3. Knowledge 4. Linguistic 5. Translation ### Detailed Analysis **1. All Categories Plot:** This plot shows heads classified into one or more categories. The distribution is densest in the later layers (approximately layers 18-30). * **Multi-Category Heads:** Pink (4 categories) and brown (3 categories) squares are scattered, primarily between layers 18-24 and heads 12-24. Purple (2 categories) squares are also present in this region. * **Single-Category Heads:** The plot is a composite of the colors from the subsequent four plots, showing the spatial overlap and segregation of different functional specializations. **2. Algorithmic Plot (Blue):** * **Trend:** Blue squares are distributed across layers ~18-30 and heads 0-30, with a notable concentration in the mid-to-lower head range (heads 12-30) of layers 24-30. * **Data Points (Approximate):** Clusters are visible around (layer 24, head 18), (layer 27, head 24), and (layer 30, head 6). The pattern is somewhat scattered but avoids the very top rows (heads 0-6) in earlier layers. **3. Knowledge Plot (Orange):** * **Trend:** Orange squares are the most sparsely distributed. They appear almost exclusively in layers 18-30 and are scattered across the head range. * **Data Points (Approximate):** Isolated points can be seen near (layer 18, head 9), (layer 21, head 21), (layer 24, head 24), and (layer 30, head 27). There is no dense clustering. **4. Linguistic Plot (Green):** * **Trend:** Green squares show a very dense and widespread distribution across layers 18-30 and heads 0-30. This appears to be the most prevalent single-category classification. * **Data Points (Approximate):** Heavy clustering is evident, particularly in layers 21-27 across almost all head indices. A dense vertical band is visible around layer 24. **5. Translation Plot (Red):** * **Trend:** Red squares are the least frequent and are confined to the highest layers (approximately 24-30) and mid-to-lower head indices (heads 12-30). * **Data Points (Approximate):** A small cluster is present around (layer 27, head 18) and (layer 30, head 21). Only a handful of red squares are visible in total. ### Key Observations 1. **Layer Specialization:** All functional specializations (Algorithmic, Knowledge, Linguistic, Translation) are almost entirely absent in the first 18 layers. Specialization emerges and intensifies in the final third of the network (layers 18-30). 2. **Category Prevalence:** The "Linguistic" category (green) is the most dominant and widespread single function in the later layers. "Translation" (red) is the most specialized and limited in scope. 3. **Multi-Function Heads:** The presence of pink, brown, and purple squares in the "All Categories" plot indicates that a subset of heads in layers 18-24 are involved in multiple functional categories simultaneously. 4. **Spatial Segregation:** While there is overlap, different categories show tendencies for different regions. For example, "Translation" heads are in higher layers and specific head ranges, while "Algorithmic" heads are more broadly distributed. ### Interpretation This visualization provides a Peircean investigation into the internal functional organization of a large language model. It suggests a hierarchical processing structure where: * **Early Layers (0-18):** Likely perform general, low-level processing not tied to these specific high-level task categories (hence "Unclassified"). * **Later Layers (18-30):** Exhibit functional specialization. The model appears to develop dedicated circuits or groups of attention heads for distinct capabilities: understanding and generating language (Linguistic), performing reasoning or calculations (Algorithmic), accessing factual information (Knowledge), and converting between languages (Translation). * **The Coexistence of Multi-Category Heads** in the transition zone (layers 18-24) may represent integrative hubs where different types of information are combined before being processed by more specialized heads in the final layers. * **The dominance of Linguistic heads** aligns with the core function of a language model, while the scarcity of Translation heads suggests this capability might be handled by a very specific, localized set of parameters or is a more emergent property. The data demonstrates that model capabilities are not uniformly distributed but are spatially organized within the network's architecture, with clear progression from general to specialized processing along the layer axis.

## Scatter Plots: Category Distribution Across Transformer Layers and Heads ### Overview The image presents five scatter plots visualizing the distribution of linguistic and cognitive categories across transformer model layers (x-axis) and attention heads (y-axis). The plots use color-coded markers to represent different categories, with a legend indicating category counts (4, 3, 2 categories) and specific linguistic/cognitive domains (Translation, Linguistic, Knowledge, Algorithmic). ### Components/Axes - **X-axis**: Layer (0-30, integer increments) - **Y-axis**: Head (0-30, integer increments) - **Legend**: - Color gradient from pink (4 categories) to gray (Unclassified) - Specific categories: - Red = Translation - Green = Linguistic - Orange = Knowledge - Blue = Algorithmic - **Subplot Titles**: - All Categories (composite) - Algorithmic - Knowledge - Linguistic - Translation ### Detailed Analysis 1. **All Categories Plot**: - Dense distribution of markers across all layers and heads - Highest concentration in layers 18-30 and heads 12-30 - Mix of all colors with gray unclassified points scattered throughout 2. **Algorithmic Subplot**: - Blue squares dominate layers 18-30 - Vertical clustering in heads 6-12 and 18-24 - Sparse points in early layers (0-12) 3. **Knowledge Subplot**: - Orange squares concentrated in layers 18-24 - Vertical banding in heads 12-24 - Fewer points in early/mid layers (0-18) 4. **Linguistic Subplot**: - Green squares show strong layer progression (18-30) - Head distribution peaks at 18-24 - Gradual increase in density toward later layers 5. **Translation Subplot**: - Red squares limited to layers 24-30 - Head concentration at 4-12 - Minimal presence in early layers ### Key Observations - **Layer Dependency**: All categories show stronger presence in later layers (18+), suggesting increased complexity in deeper transformer blocks - **Head Specialization**: - Algorithmic: Dominates middle heads (6-12, 18-24) - Translation: Concentrated in lower heads (4-12) - Knowledge: Spread across middle heads (12-24) - **Category Co-occurrence**: - Green (Linguistic) and orange (Knowledge) markers frequently overlap in layers 18-24 - Blue (Algorithmic) appears independently in deeper layers - **Unclassified Points**: - 12 gray markers in All Categories plot - Mostly in layers 12-24, heads 6-18 ### Interpretation The data reveals systematic patterns in how different cognitive/linguistic functions are distributed across transformer architecture: 1. **Hierarchical Processing**: - Early layers (0-18) show general linguistic processing (green) - Middle layers (18-24) specialize in knowledge integration (orange) - Late layers (24-30) focus on translation-specific tasks (red) 2. **Head Specialization**: - Lower heads (0-12) handle basic translation tasks - Middle heads (12-24) manage knowledge integration - Upper heads (18-30) specialize in algorithmic processing 3. **Unclassified Activity**: - The presence of gray points suggests residual processing not captured by current categorization - Concentration in middle layers/heads may indicate transitional processing stages 4. **Architectural Implications**: - The clear layer progression suggests effective hierarchical feature learning - Head specialization patterns align with transformer's parallel processing capabilities - Knowledge/linguistic overlap in middle layers may reflect semantic integration mechanisms This visualization provides empirical evidence for the modular organization of transformer models, with distinct functional specialization across both layers and attention heads.